WITH the General Election ending in a hung parliament, there could be days or weeks of political horse-trading before the final form of the next government is settled.

No party has emerged with an overall majority meaning the incumbent Conservative Government stays in office until Theresa May either does a deal - most likely with the Democratic Unionists - or goes to the Queen to tender her resignation and that of her administration.

If the latter happens, Jeremy Corbyn as leader of the largest opposition party may be invited by the Queen to form a government either as a minority or in coalition with another party or parties.

In 2010, Gordon Brown held onto the premiership for six days as frantic negotiations took place, resigning only when it became clear that the Conservatives and Liberal Democrats had reached agreement on a viable coalition.

It is highly likely that Mrs May too would hold back on any resignation until she has had time to test whether she has the support to attempt to continue in office.

With 650 MPs in Parliament, 326 seats are needed for an absolute majority in the House of Commons.

But in practice, a working majority will require just 322 MPs, as the Speaker does not vote and Sinn Fein has so far declined to take up its seats.

Mrs May would be able to pass this crucial figure with the support of the DUP but the Ulster party will demand significant concessions in return for propping up her adminstration.

The Brexit-supporting party has boosted its number to 10 with two gains, giving it a potentially pivotal role.

Meanwhile, Mr Corbyn's Labour would be expected to explore the potential for co-operation with other "progressive" parties like the Lib Dems, Scottish National Party, Plaid Cymru and the Green Party's sole MP Caroline Lucas.

In sharp contrast to 2010, a whole series of parties have already forsworn any involvement in a formal coalition, apparently making this outcome unlikely.

Labour has said it will not seek a coalition, instead seeking to govern as a minority government if possible. And Liberal Democrat leader Tim Farron pledged during the election not to go into coalition with either the Tories or Labour.

But other arrangements short of a coalition could involve a "supply and confidence" agreement under which smaller parties would pledge to back the Government's budget and programme without taking up ministerial positions in the new administration.

Or, either the Conservatives or Labour could attempt to govern as a minority administration, seeking to win support in the Commons for their programme on a vote-by-vote basis.

The first milestone for Mrs May would be June 13, when the House of Commons is due to return after the election. But a far more significant deadline is the Queen's Speech on June 19, when the sovereign will read out the legislative programme of the new government.

Any Prime Minister would be unlikely to ask the Queen to present a programme if they did not believe it would secure the support of a majority of MPs in the Commons.

The Cabinet Manual drawn up in 2010 following the inconclusive result of that year's election states that the incumbent government is "entitled to wait until the new Parliament has met to see if it can command the confidence of the House of Commons, but is expected to resign if it becomes clear that it is unlikely to be able to command that confidence and there is a clear alternative".

Without a clear alternative, the parties would be expected to hold discussions to establish whether any of them is able to form an administration capable of commanding the confidence of the Commons. The Prime Minister can authorise the civil service to provide support in negotiations, as they did in 2010.

The Queen would not expect to become involved in any negotiations, but the Palace would be kept informed via representatives of the political parties or the Cabinet Secretary.

If no viable administration can be constructed which would be capable of getting its budget and its programme through Parliament, then voters could be asked to return to the polling stations for the third general election in as many years.